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Determinism and Predicting Machine

This is a copy of the article Determinism and Predicting Machine by Daniel Gogol. It appeared in the philosophical journal Philosophy and Phenomenological Research, Vol. 30, No. 3 (Mar., 1970), pp. 455-456

“Determinism is sometimes thought to entail the theoretical possibility of total knowledge. A strongly deterministic position is, that all physical events conform to a set of laws, and that if sufficient data were given about the state of the universe at a given instant, the occurrence or non-occurrence of a given future event could be deduced from these laws. Related to this strongly deterministic position is the question of the theoretical possibility of building a machine to predict the future.

We present an argument whose outcome is that it is impossible for a certain type of predicting machine to exist.

Assume that a machine could exist, called machine M, such that there is some amount of time, t hours, and some distance, d feet, such that the machine would correctly answer any question given it as long as the question had a “yes” or “no” answer and was about the occurrence or nonoccurrence of a physical event within t hours and within d feet of the machine. Assume also that the machine’s answer would consist of some physical event occurring within t hours and within d feet. For example, it might be built to type “yes” or “no”, depending on the correct answer to the question.

Now suppose that the machine were asked the following question: “Will the machine M answer ‘no’ before answering ‘yes’, and at some time during the next t hours?”

Now since this is a question with a “yes” or “no” answer about future physical events occurring within d feet and within t hours, the machine will answer “yes” or “no” within the next t hours. But if it answers “yes”, then the correct answer is “no”, and if it answers “no”, then the correct answer is “yes”. Therefore, by assuming the existence of a machine with certain properties we have been led to a contradiction, so we must reject the existence of such a machine as a logical impossibility.

Of course, the philosophical implications of the impossibility of such a machine are sharply limited. The argument used does not show, for instance, that a machine could not be built which could deduce whether or not any given physical event would occur within 24 hours. But such a machine could not also have the property that it always provided the answer within 24 hours.

Also, our argument does not show that a machine could not be built to answer all but certain special questions, such as the one in our argument. but it would seem that if a complete set of physical laws did exist, such that the answer to all questions of a certain type could be deduced from a sufficient data, then a machine which provides the answers should be theoretically possible, so that the fact that it is not possible destroys some of the plausibility of the idea that such a complete set of physical laws exists. If such a complete set of laws does exist, then it is a “physical” impossibility to build a machine to collect sufficient data and make the necessary deductions fast enough to have the properties of machine M.

Our argument about machine M applies to other possible universes as well as our own, and in different possible universes machine M may be impossible for different reasons. We could divide possible universes into the following two classes:

(1) Those possible universes in which there does not exist a set of physical laws such that any given future physical event can be logically deduced if there is sufficient data about the present physical state of the universe.”

(2) Those possible universes in which there is such a set of physical laws, but it is a physical impossibility to build a machine with the properties of machine M.